Chapter 1 Introduction
4.4 Cumulative PNLFs and stellar populations in the M31 disc and inner halo
4.4 Cumulative PNLFs and stellar populations in the M31 disc and inner halo 85
Table 4.3: Comparison of PNLF shapes for regions in M 31 with the Anderson-Darling test. The null hypothesis that the two PNLF shapes come from the same distribution is rejected at a given significance level. The value is floored/capped at 0.1%/25%. In this work, we reject the null hypothesis when the significance level less than 5%. In such cases, the region mentioned in the second column and the significance level are marked in italics in the table.
Regions compared Significance level (%) Disc (10<RGC≤20 kpc) Disc (20<RGC≤30 kpc) 4.1
Giant Stream 0.2
NE-Shelf 0.1
G1-Clump 0.1
W-Shelf 0.2
Stream-D 0.1
Disc (20<RGC≤30 kpc) Giant Stream 2.8
NE-Shelf 0.1
G1-Clump 1.0
W-Shelf 0.2
Stream-D 0.1
Giant Stream NE-Shelf 25.0
G1-Clump 25.0
W-Shelf 9.0
Stream-D 0.1
NE-Shelf G1-Clump 25.0
W-Shelf 14.5
Stream-D 0.7
G1-Clump W-Shelf 25.0
Stream-D 4.4
W-Shelf Stream-D 18.1
and not solely driven by the PNe in the faintest magnitude bin in the cumulative PNLFs, with the significance level well below 5%. The exception is the comparison of the Disc (20<RGC≤30 kpc) and Giant Stream regions, where the significance level increases to 9%.
4.4 Cumulative PNLFs and stellar populations in the M31
Figure 4.6: The [M/H] value for the different regions in M31 and the LMC is plotted against the M∗value obtained from fitting their PNLF. The different markers show the different references for the [M/H] measurements – circle: Williams et al. (2017); pentagon: Bernard et al. (2015);
triangle: Escala et al. (2020); inverted triangle: Nidever et al. (2020); cross: Tanaka et al. (2010);
square: Conn et al. (2016). The theoretical expectation from Dopita et al. (1992) is shown with the dotted line.
sub-regions and also for the LMC. We note that [M/H] measurements are also available from spectroscopy of individual RGB stars for some of the regions.
4.4.1 The absolute magnitudes of the PNLF bright cut-o ff and their de-pendency on [M / H]
The measured absolute magnitudesM∗for the PNLF bright cut offin different galaxies show that such quantities do not depend on morphology, star-formation histories and ages (Ciardullo et al.
2013), but their values depend on the metallicity of the parent stellar population (see Ciardullo et al. 2002). We examine the dependency ofM∗on the [M/H] of the parent stellar population for the distinct M 31 regions and the LMC. We list the best-fitting M∗values along with the [M/H]
values of the parent stellar populations from the literature, in Table 4.2.
4.4 Cumulative PNLFs and stellar populations in the M31 disc and inner halo 87
In general, the photometrically measured [Fe/H] is taken to be equal to the [M/H] value, as [α/Fe] is assumed to be zero for the fitted isochrones (e.g. Bernard et al. 2015; Conn et al. 2016;
Williams et al. 2017). The [M/H] for the 10<RGC ≤20 kpc disc region is obtained as the mean [M/H] from the PHAT photometry, covering a third of the M 31 disc at this radii, by Williams et al. (2017). The [M/H] for the the NE-Shelf and G1-Clump regions is from the pencil-beam HST photometry by Bernard et al. (2015). For Stream-D, the [M/H] measurement is from the CFHT MegaCam observations, covering this entire sub-region, by Conn et al. (2016). The [M/H]
for the 20<RGC ≤30 kpc disc region and the Giant Stream4 are obtained from the mean [Fe/H]
and mean [α/Fe] values measured from individual stars in small fields observed in these regions by Escala et al. (2020). These values are converted to [M/H] using the following relation from Salaris & Cassisi (2005):
[M/H]∼ [Fe/H]+log(0.694×10[α/Fe]+0.306) (4.6) We note that the spectroscopic [M/H] for these two regions agree within errors with that from the pencil-beam HST photometry in these regions by Bernard et al. (2015). For the LMC, we derive the median [M/H] value from the median [Fe/H] and median [α/Fe] values for APOGEE RGB stars spanning a large radial range in the LMC (Nidever et al. 2020). For the W-Shelf, Tanaka et al. (2010) construct CMDs for the resolved stellar population in the Subaru Supreme-Cam pointings. The mean [Fe/H] value is measured photometrically from isochrone-fitting to the W-Shelf CMD, assuming [α/Fe]=0.3. We use the measured [Fe/H] and assumed [α/Fe] value in Equation 4.6 to obtain the measured [M/H] for the W-Shelf. In Figure 4.6, we show theM∗ values for different M 31 regions against their [M/H] values.
In Figure 4.6, we also depict the theoretical variation of M∗with [M/H]. This was computed from the variation of M∗ with [O/H] obtained by Ciardullo et al. (2002) from the Dopita et al.
(1992) PN evolution models. [O/H] is calibrated to [M/H] by subtracting the solar [O/H] value (=8.69; Asplund et al. 2009) as it is done for calibrating stellar and gas phase mass-metallicity relations of galaxies (e.g. Zahid et al. 2017). We find that the fittedM∗for the LMC, the two disc regions, the G1-Clump and the NE-Shelf are in agreement with the theoretical expectation from Dopita et al. (1992). However, theM∗for the PN samples in Giant Stream, W-Shelf and Stream-D areas are fainter than those predicted on the basis of the measured [M/H] of their parent stellar populations.
Given the low surface-brightness of the Stream-D and W-Shelf substructures and the short visibility lifetimes of PNe (Buzzoni et al. 2006), it is possible that the small number of detected PNe are not seen at their brightest but rather once they faded. This may possibly explain faded M∗values for the Stream-D and W-Shelf. This is not the case for the Giant Stream which is a brighter substructure with a larger number of detected PNe. In the case of the Giant Stream, the brightest PN has an absolute magnitude M∗5007 = −3.51 with 12+(O/H)= 8.3 dex (PN14 from
4The metallicity gradient in the Giant stream is studied by Conn et al. (2016). In their Figure 3, they show the spatial coverage of their fields and give the corresponding [Fe/H] (=[M/H] as [α/Fe]=0) values in their Table 1.
With this PNe survey, we cover a spatial area in the Giant Stream corresponding to their mean metallicity range of [M/H]=−0.4 to−0.7. The [M/H] value for the Giant Stream from Escala et al. (2020) covers the metallicity range observed by Conn et al. (2016) within error and is thus an accurate [M/H] value for parent population of the PN subsample in the Giant Stream.
Figure 4.7: Linear relation between the slope of exponential function at the faint end of the PNLF,cf2, and the percentage stellar mass formed within the last 5 Gyr,m∗, <5 Gyr.
Fang et al. 2018), corresponding to [M/H]= −0.39. Thus it is spectroscopically confirmed that the PN at the PNLF bright cut-off in the Giant Stream has a metallicity value consistent with those obtained by Escala et al. (2020) for the resolved RGBs.
To comprehend the fainter M∗ for the Giant Stream, given its measured [M/H] value, metal-licity and other possible effects influencing PN evolution need to be re-evaluated. This is par-ticularly important given the significance of the absolute magnitude of the PNLF bright cut-off, M∗, as a reliable secondary distance indicator across the different Hubble galaxy types (Ciardullo et al. 2013).
4.4.2 Imprint of star-formation history on the very faint-end of the PNLFs in M 31
Bernard et al. (2015) obtained the SFHs in 14 deep HST pointings in different regions of the M 31 disc and some of the inner halo substructures. While they found that M 31 had a ubiquitous burst of star formation∼ 2 Gyr ago, they measured significant differences in the percentage of
4.4 Cumulative PNLFs and stellar populations in the M31 disc and inner halo 89
Table 4.4: Percentage stellar mass formed within the last 5 Gyr, m∗, <5 Gyr, from the PNLF pre-dicted with the pick-one-out test. The m∗, <5 Gyr in the HST fields corresponding to the LMC, Disc (10-20 kpc) and all other regions are from Weisz et al. (2013), Williams et al. (2017) and Bernard et al. (2015) respectively. Them∗, <5 Gyrvalues are predicted for each region from itscf2
value by fitting the relation betweencf2andm∗, <5 Gyrfor all the other regions except the selected region.
Region m∗, <5 Gyr
HST CMD PNLF prediction LMC 50.1±3.3 49.94±11.98 Disc (10-20 kpc) 27.1±3.7 20.02±6.55 Disc (20-30 kpc) 14.7±5.1 9.15±11.02 Giant Stream 10.2±8.4 18.04±9.22 NE-Shelf 11.1±5.7 13.49±5.78 G1-Clump 29.3±4.2 32.23±2.77
W-Shelf N.A. ≤42.19
Stream-D N.A. 27.14±9.46
stellar mass formed<5 Gyr ago (hereafterm∗, <5 Gyr) in distinct HST fields aligned with different substructures. In particular, they found that HST pointings in the Giant Stream, NE-Shelf and outer disc have much smaller m∗, <5 Gyr compared to the G1-Clump. Based on these SFHs, they termed the Giant Stream and NE-Shelf asstream-like, while the G1-Clump was termed as disc-like. The outer-disc field was labeled as a composite field, having a slightly larger m∗, <5 Gyr
value compared to thestream-likefields. No SFH measurements are available for the W-Shelf5 and Stream-D. Williams et al. (2017) utilized observations from the PHAT survey (Dalcanton et al. 2012) to find that∼ 10−20% of the stellar mass within a galactocentric radius of 20 kpc is formed in a burst of star-formation ∼ 2 Gyr ago with m∗,<5Gyr ∼ 30%. Using their HST observations in 8 scattered fields in the LMC, Weisz et al. (2013) showed that ∼ 50 % of the stellar mass in the LMC was formed in the last 5 Gyr.
Given the extended coverage of the HST fields utilised to measure the average SFH from resolved stellar populations in the LMC and the M 31 10<RGC≤20 kpc disc region, the measured m∗, <5 Gyr value is representative of the average stellar population in these regions. Since the average SFH of the parent stellar population leaves an imprint on the global PNLF of any region, the measured m∗, <5 Gyr value for the aforementioned regions can be linked to their PNLF fit parameters. For the other four regions (see Figure 4.1), the SFH measured from the pencil-beam HST fields obtained by Bernard et al. (2015) may not be representative of the average one for the entire substructures (Williams et al. 2017).
However, we can assess whether the SFH values determined from the pencil-beam HST fields are representative of the average values for the entire stellar population in any substructure by checking whether the relation between the global PNLF parameters and the measuredm∗, <5 Gyr 5The HST field linked to the W-Shelf by Bernard et al. (2015) does not overlap with the W-Shelf spatial over-density as obtained by PAndAS (McConnachie et al. 2018).
value for these regions lie on the same relation as that for the average SFH of the LMC and the M 31 10<RGC≤20 kpc disc region. Any region whose average SFH value is vastly different from that found within the tiny HST pointing would diverge significantly from any fitted relation.
We find a correlation between the percentage stellar mass from the HST fields in two age bins (see Table 4.4), younger and older than 5 Gyr following the age distinction by Bernard et al.
(2015), and the exponential function fitting to the faint-end of the PNLF, cf2 (see Table 4.2).
Figure 4.7 showscf2 againstm∗, <5 Gyr in any HST field of a given sub-region. We find that the sub-regions whose SFH value is obtained from large spatial HST coverage lie tightly on the same relation as those regions with smaller fields. Fitting the relation between m∗, <5 Gyr andcf2 with a linear function using a Deming regression6(Kummell 1879), the best fit is given by:
m∗, <5 Gyr= −5.38 (±0.54) × cf2 + 53.07 (±2.48) (4.7) Since it is not known a priori the HST field of which region would be an outlier influencing the fitted parameters of Equation 4.7, we run a “pick-one-out test” over the parameters for the six regions. The relation betweencf2 and m∗, <5 Gyr is fitted for five of the six regions and the m∗, <5 Gyrvalue is predicted for the selected region from itscf2 value. This process is iterated for each of the six regions. The predictedm∗, <5 Gyrvalues are noted for each region in Table 4.4. The predicted quantities are in good agreement with those measured from the HST fields implying that the cf2 – m∗, <5 Gyr relation is applicable to the entire parent stellar population of the PNe in any region. We thus also use Equation 4.7 to predict them∗, <5 Gyr values for the W-Shelf and Stream-D (Table 4.4) also.
4.4.3 Stellar population dominating the very faint-end of the PNLF
Following this analysis, we infer that thecf2value of the PNLF increases linearly with decreasing fraction of the stellar mass of its parent stellar population that formed in the last 5 Gyr. Hence, the rise at the faint-end of the PNLF is driven by the fraction of the stellar mass in the stellar population older than 5 Gyr. This is in agreement with the expectations from the post-AGB stellar evolution models by Marigo et al. (2004) where the faint-end of the PNLF is populated by PNe evolving from older stellar populations and powered by less-massive central stars (see their Figures 18 & 25 and associated text). However, it is in contrast to the predictions by M´endez et al. (2008) where the faint-end of the PNLF is populated by PNe from massive progenitor stars from young stellar populations which have faded rapidly while losing their envelope.